This notion generalizes hyperbolic geometry by formalizing the observation that,
in a non-positively curved space, triangles with geodesic sides appear to be
thinner than in usual, flat, spaces. Its importance is due to the numerous
applications this notion has allowed. We only mention basic notions here, and
refer the reader to standard texts for a more detailed presentation of the
subject [1]}, [2]}, [3]}.
In the rest of this section, for simplicity, we only consider symmetric
generalized metric spaces, since the topology of a space does not depend on its
direction. Interesting possible generalizations in the directed case are
mentioned in Section .
